Entanglement for Pattern Learning in Temporal Data with Logarithmic Complexity: Benchmarking on IBM Quantum Hardware

Time series forecasting is foundational in scientific and technological domains, from climate modelling to molecular dynamics. Classical approaches have significantly advanced sequential prediction, including autoregressive models and deep learning architectures such as temporal convolutional networks (TCNs) and Transformers. Yet, they remain resource-intensive and often scale poorly in data-limited or hardware-constrained settings. We propose a quantum-native time series forecasting framework that harnesses entanglement-based parameterized quantum circuits to learn temporal dependencies. Our Quantum Time Series (QTS) model encodes normalized sequential data into single-qubit rotations and embeds temporal structure through structured entanglement patterns. This design considers predictive performance with logarithmic complexity in training data and parameter count. We benchmark QTS against classical models on synthetic and real-world datasets, including geopotential height fields used in numerical weather prediction. Experiments on the noisy backend and real IBM quantum hardware demonstrate that QTS can capture temporal patterns using fewer data points. Hardware benchmarking results establish quantum entanglement as a practical computational resource for temporal modelling, with potential near-term applications in nano-scale systems, quantum sensor networks, and other forecasting scenarios.